# Tagged Questions

Questions on the statistical functions of Mathematica.

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### Estimate error on slope of linear regression given data with associated uncertainty

Given a set of data, is it possible to create a linear regression which has a slope error that takes into account the uncertainty of the data? This is for a high school class, and so the normal ...
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### Simultaneously fitting multiple datasets

What is the proposed approach if one wants to simultaneously fit multiple functions to multiple datasets with shared parameters? As an example consider the following case: We have to measurements of ...
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### Histograms with pre-counted data

I've got some large data sets which have been counted but not binned already - essentially, a list of pairs of values (not bins) and counts.* (Or, equivalently, it's been binned into too-small bins.) ...
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### Standard errors for maximum likelihood estimates in FindDistributionParameters

I am trying to fit a non-standard PDF to data and FindDistributionParameters works great, and gives me the parameters of the distribution back using maximum ...
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### How to use a 3×3 covariance matrix to plot an error ellipsoid?

I have a 3×3 error covariance in Mathematica, but I don't know how to use it for plotting the error ellipsoid. It would be great if you can show me how I can do that for the below covariance matrix: ...
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### Efficiently generating n-D Gaussian random fields

I am interested in an efficient code to generate an $n$-D Gaussian random field (sometimes called processes in other fields of research), which has applications in cosmology. I wrote the following ...
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### Showing the correlation of two variables using a plot

I have a list of $\{x_i,y_i\}$ pairs and I want to show that $x_i$'s and $y_i$'s have positive correlation. The result of ...
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### Which Distributions can be Compiled using RandomVariate

Recently, Oleksandr kindly showed a list of Mathematica commands that can be compiled. RandomVariate was part of that list. However, whether this can be compiled depends upon the distribution that is ...
1k views

### Finding distribution parameters of a gaussian mixture distribution

Short version: how to estimate the parameters of a mixture of multivariate normal distributions (i.e.: Gaussian mixture model)? Long version. I am trying to estimate the parameters of a mixture of ...
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### Performing a chi-square goodness of fit test

How would I perform a chi-square goodness of fit test? I have tried the following, where my data consists of the observed values whilst the data pair contains the correct values. Then I use the ...
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### Testing for OLS Heteroscedasticity White's General Test

I've done my best to search the help and google White's test (http://en.wikipedia.org/wiki/White_test) in Mathematica. Can anyone point me to a function or Mathematica reference for this or do you ...
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### How does Mma compute Confidence Intervals?

I am trying to understand how Mma computes the Confidence Intervals after a NonlinearModelFit. Consider the following example: ...
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### Representative Smooth Kernel Distribution from Truncated Distribution

I am trying to produce a better distribution from a dataset that is bounded to be greater than 0. Here is an example distribution from the documentation that mimics the behavior of the actual dataset: ...
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### How does LocationTest choose its “AutomaticTest”?

Is there a way of determining how LocationTest chooses its "AutomaticTest"? Sometimes it's clear from the ...
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### Grain(Particle) Size Distribution (PSD) Analysis with Mathematica

I would like to do an analysis of the grain size distribution of a Monte Carlo Grain Growth simulation I implemented based on the nice example by Rituraj Nandan (see Link). The result of this ...
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### How to partition a list into sublists in a similar way to Histogram

I have a list of list as below (I show part of it) ...
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### Plot Ellipse based on EigenSystem

Please consider the following : ...
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### Unexpected behavior of confidence bands for data presenting two regions with uneven noise

Let's generate some noisy data with uneven noise. ...
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### Doing a chi-square independence test in Mathematica

I have a matrix consisting of the following data: Needs["HypothesisTesting`"] data = {{11, 206}, {32, 1374}} How would I make a chi-square independence test ...
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### How to augment the realm of functions Mathematica thinks it knows how to integrate symbolically

My question involves extending the functionality of Integrate over specific integrals in the most generic manner. Specifically, is it possible to "hack into" ...
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### Hodrick–Prescott filter (one-sided version)

I am interested in implementing Hodrick–Prescott filter (HP filter) on my time series data in Mathematica. I know that there is already a version of two-sided original filter for Mathematica (see ...
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### Visualization: elliptical insights into data sets…

I was recently reading the following paper on visualization techniques using ellipses to gain statistical insights. Elliptical visualization for looking at correlations has briefly been touched on ...
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### Detecting and counting signals in list data: checking pulse rate

Hope this isn't too much of a basic question: I'm looking for some Mathematica functions, but I don't know which ones. Background I recently read about a simple technique for reading your body's ...
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### Measure a DensityHistogram[] pair similarity

I study human vision and more specifically eye-movements. "If we display 2 symmetrical patterns (20 min one after the other), will our gaze distribution be symmetric is my research question." The 2 ...
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### How to efficiently find moments of a multinormal distribution?

I have a multinormal distribution with covariance matrix $\sigma$ and zero mean. I want to find moment $$E[x_1^{r_1}x_2^{r_2}\cdots x_n^{r_n}] =\,?$$ Of course, there is a build-in function ...
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### Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
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### Different calculation of median and quartiles, bug in BoxWhiskerChart?

When you plot a dataset with BoxWhiskerChart passing over the box in the plot with your mouse pointer shows some specifics about the dataset (min and max values, ...
162 views

### Inconsistent DistributionFitTest results?

In pondering this question, I used Mariana's function to generate the following data. ...
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### How can I tell mathematica to generate an histogram from nominal data?

If I write: Histogram[{1, 1, 1, 2, 2, 2}] I get a nice histogram chart but if I write ...
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### What is the Mathematica equivalent for the Excel function tinv()?

TINV() returns the t-value of the Student's t-distribution as a function of the probability and the degrees of freedom. For example ...
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### Most efficient way to obtain samples from high-dimensional multivariate distributions?

Is MultinormalDistribution[] efficient and easy to use for high dimensions? I have a variable $n$ representing the dimension of a Monte Carlo integration I do on a ...
371 views

### BoxWhiskerChart with logarithmic axes

I would like to make a following chart Ideally I would also like to control the boxes position on a logarithmic x-axis. Some inspiration how to do the latter may be found in the answer to my ...
108 views

### Best way to represent a joint distribution

The motivation for this question is producing a distribution that produces the gender and age of an individual when the distribution of ages depends on gender. Suppose I want a distribution which, ...
2k views

### Function for Autocorrelation

Is there a built in function to compute the autocorrelation of a signal ?
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### Given two samples, how does LocationTest select its AutomaticTest?

How does LocationTest select its "AutomaticTest" when testing two samples? Background: A previous post poses a similar question ...
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### BoxWhiskerPlot - how to specify boxes position on the horizontal axis

Let's say I have a folowing set of data: k = 1 : list of values k = 3 : list of values k = 10 : list of values I know that to make a BoxWhiskerChart I have to ...
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### Fitting data to an ARProcess using FindProcessParameters

I have 50 data points that I would like to represent as an AR(4) process. I'd like to over-plot the behaivor of the estimated process model with that of the original (raw) data before I use the model ...
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### stationary distribution of a transition matrix

How can I solve the stationary distribution of a finite Markov Chain? In other words, how can I estimate the eigenvectors of a transition matrix?
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### I need a technique for determining and drawing a line where the density in a listplot jumps up suddenly

Basically I have a two dimensional list plot with a bunch of points between the square of (0,0) and (1,1). The y-values of these points are drawn from a uniform probability distribution between 0 and ...
2k views

### Filtering Lists in Mathematica [duplicate]

Possible Duplicate: Select/Delete with Sublist elements? I need help in filtering long lists of x,y coordinates.Lets use the following list as an ...
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### On Parameter Estimation using FindDistributionParameters

I am a novice of Mathematica and have recently started my self-study of maximum likelihood estimation (MLE) using Mathematica. I would like to estimate the parameters associated with a distribution ...
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### Extracting Imported Information

What I want to do is to compare the relationship between the consumption of say beer and wine using scatter plots where each point designates the particular country (preferably named). I have tried to ...